A circus artist drops a ball from a high wire. The ball takes 1.5 seconds to reach the ground.
I) Find the height of the height of the high wire above the ground.
II) Write an expression for the speed of the ball t seconds after being dropped where 0<t<1.5
III) How fast is the ball moving as it hits the ground
please help. Thanks
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I) To find the height of the high wire above the ground, we can use the formula for the distance an object falls due to gravity:
Distance = 1/2 * g * t^2
Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth. In this case, since the ball takes 1.5 seconds to reach the ground, we can substitute t = 1.5 into the formula:
Distance = 1/2 * 9.8 * (1.5)^2
= 1/2 * 9.8 * 2.25
= 11.025 meters
Therefore, the height of the high wire above the ground is approximately 11.025 meters.
II) To find an expression for the speed of the ball t seconds after being dropped where 0 < t < 1.5, we need to calculate the velocity of the ball at time t. The velocity can be determined using the formula:
Velocity = g * t
Using g = 9.8 m/s^2, the expression for the velocity of the ball is:
Velocity = 9.8 * t
III) As the ball hits the ground, its velocity will be its final velocity. From previous calculations, we know that it takes 1.5 seconds for the ball to reach the ground. Therefore, the final velocity of the ball is:
Velocity = 9.8 * 1.5
= 14.7 m/s
Hence, the ball is moving at a speed of 14.7 m/s as it hits the ground.